JEE MAIN - Physics (2014 (Offline) - No. 19)
One mole of a diatomic ideal gas undergoes a cyclic process $$ABC$$ as shown in figure. The process $$BC$$ is adiabatic. The temperatures at $$A, B$$ and $$C$$ are $$400$$ $$K$$, $$800$$ $$K$$ and $$600$$ $$K$$ respectively. Choose the correct statement :
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The change in internal energy in whole cyclic process is $$250$$ $$R.$$
The change in internal energy in the process $$CA$$ is $$700$$ $$R$$.
The change in internal energy in the process $$AB$$ is - $$350$$ $$R.$$
The change in internal energy in the process $$BC$$ is - $$500$$ $$R.$$
Explanation
In cyclic process, change in total internal energy is zero.
$$\Delta {U_{cyclic}} = 0$$
$$\Delta {U_{BC}} = n{C_v}\Delta T = 1 \times {{5R} \over 2}\Delta T$$
$$\Delta {U_{cyclic}} = 0$$
$$\Delta {U_{BC}} = n{C_v}\Delta T = 1 \times {{5R} \over 2}\Delta T$$
where, $${C_v} = $$ molar specific heat at constant volume.
For $$BC,$$ $$\Delta T = - 200\,K$$
$$\therefore$$ $$\Delta {U_{BC}} = - 500R$$
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